In the field of design support, there is a technique for obtaining an objective function in multi-objective optimization design supporting technologies and the like, which are employed in designing a shape of a slider included in a hard disk, and the like. Along with the increasing packaging density and storage capacity of hard disks, an amount of distance between a magnetic disk and a header of such a hard disk has become increasingly small. Therefore, it has been demanded to design a slider so as to reduce an amount of variation of flying of the slider, which arises due to an altitude difference and disk radius position of the slider.
As shown in FIG. 13, a slider denoted by an a reference numeral 1301 is equipped at the bottom part of the tip of an actuator 1302 which moves over a magnetic disk mounted inside a hard disk, and the position of a header is calculated from the shape of the slider 1301.
In design problems in engineering, several conditions are given that should be met simultaneously. When determining an optimum flying performance of the slider 1301, it is necessary to efficiently improve performance such as flying height (1303 of FIG. 13), roll (1304) and pitch (1305) which are concerning the position of the header and represented by mathematical functions associated with shape-related parameters.
To solve such a type of problems, multi-objective optimization methods are used. In almost all cases, it is impossible to optimize all the objective functions simultaneously. There is a trade-off relation between them, i.e., it is only possible to improve one objective function at the cost of another. In a multi-objective optimize problem, the points that cannot be improved in all the objective functions at the same time form an optimal set called a Pareto optimal front.
Up to now, multi-objective optimization problems have not been directly handled, but, as shown in the following formula, single-objective optimizations have been performed, in which a linear summation f of individual terms obtained by multiplying an objective function f_i by a weight m_i is calculated to obtain a minimum value of the linear summation f.f=m—1*f—1+ . . . m—t*f—t 
Further, by executing a program, processing has been performed so that, in conjunction with gradual small changes of respective values of parameters p, q, r and the like shown in FIG. 14, which determine a shape S of a slider, output values of the function f are calculated, and from the calculated output values thereof, a shape of the slider having values of the parameters p, q, r and the like which make the output values of the function f to be minimum is derived.
Here, the function f depends on the weight vectors {m_i}. In actual designs, processing has been performed so that, in conjunction with gradual changes of the weight vectors {m_i} which are further made, minimum values of the function f for respective changed values of the weight vectors {m_i} are calculated, and by making a comprehensive decision regarding balancing of respective minimum values of the function f and the corresponding values of the weight vectors {m_i}, a shape of the slider is determined.
Furthermore, methods including a method which is called the normal boundary intersection (NBI) method, and the like, have been also known to those skilled in the art, the methods enabling obtaining of a Pareto curved surface (an optimized curved surface) in the multi-objective optimization by using a numerical analysis scheme. Japanese Laid-open Patent Publication No. 2002-117018 discloses a related technique.
However, in the foregoing optimization technology associated with a single objective function f in existing technologies, it is necessary to iteratively perform flying calculations which require a large amount of time. Particularly, further detailed research for a shape of a slider requires input parameters (corresponding to parameters p, q, r and the like shown in FIG. 14) whose number is around twenty, thus, more than ten thousand cycles of flying calculations, and leads to a disadvantage in that it takes a significantly large amount of time to perform optimization of a shape of a slider.
For example, FIG. 15 is an operational flowchart of processing performed by a system using existing technologies. Subsequent to setting of specifications (step S1501) and setting of weight vectors (step S1502), in calculations with respect to processing for optimization of a single objective function (step S1503), it is necessary to perform a huge number of calculations for around several ten thousand groups of input parameters.
Further, in this method, a minimum value of the function f (as well as the values of input parameters as of then) depends on how to determine the weight vectors (m_1, . . . , m_t). In actual designs, a situation, in which it is desired to compare values of the function f resulting from performing optimization of the function f for various groups of weight vectors, occurs frequently. However, in the foregoing existing technologies, returning the flow of iterative processing from step S1504 to step S1502 shown in FIG. 15 for every group of changed weight vectors makes it necessary to restart a series of optimization calculations including calculations with respect to flying height, which incur high cost. Therefore, the number of kinds of weight vectors which can be proved is restricted. Accordingly, it takes an enormous time to determine final weight vectors (step S1505 in FIG. 15) and obtain the output of an optimum shape (a group of optimum parameters) of the slider (step S1506 in FIG. 15).
Moreover, in each of processes of minimizing the values of the function f, it is possible to obtain only one point, which makes the values of the function f to be minimum, on a Pareto curved surface, thus, causing a disadvantage in that, it is difficult to estimate optimum mutual relations among objective functions, and therefore, it is impossible to feed back design related information, such as a piece of information related to the mutual optimum relations among objective functions, to the design.
Furthermore, the forgoing existing technologies, in which the Pareto curved surface is obtained by using the numerical analysis scheme, have disadvantages in that, in the case where a feasible region is a non-convex region, the Pareto curved surface cannot be solved, and further, in the case where an original point (a termination point) necessary for obtaining the Pareto curved surface is close to the targeted Pareto curved surface, sometimes, algorithms employed in the numerical analysis cannot function in an expected manner.